## Bill is 2 years older than his brother Will. If the product of their ages is one less than five times the sum of their ages, how old are Bil

Question

Bill is 2 years older than his brother Will. If the product of their ages is one less than five times the sum of their ages, how old are Bill and Will?

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2 weeks 2021-09-08T08:25:41+00:00 1 Answer 0

Will’s age = 9 years

Bill’s age = 11years

Step-by-step explanation:

Let will age = x

Bill = x +2 since he is 2 years older

x(x+2) = 5( x +x+2) – 1

Opening brackets

x² + 2x = 5(2x + 2) – 1

x² + 2x = 10x + 10 – 1

x² + 2x = 10x + 9

Collect like terms

x² + 2x – 10x – 9 = 0

x² – 8x – 9 = 0

Solve quadratically using factorisation method by finding two factors of +9 that can add up to give -8, the coefficient of x.

The factors are -9 and +1

x² + x – 9x – 9 = 0

x(x + 1) -9( x +1)

x+1) (x -9) =0

x + 1 = 0 or x -9 =0

x = -1 or 9

Age can not be negative

Therefore,

Will’s age = 9 years

Bill’s age = x+2 = 9+2 = 11years